A comprehensive study of the discovery potential of NOvA, T2K and T2HK experiments

With the recent measurement of reactor mixing angle $theta_{13}$ the knowledge of neutrino oscillation parameters that describe PMNS matrix has improved significantly except the CP violating phase $delta_{CP}$. The other unknown parameters in neutrino oscillation studies are mass hierarchy and the octant of the atmospheric mixing angle $theta_{23}$. Many dedicated experiments are proposed to determine these parameters which may take at least 10 years from now to become operational. It is therefore very crucial to use the results from the existing experiments to see whether we can get even partial answers to these questions. In this paper we study the discovery potential of the ongoing NO$ u$A and T2K experiments as well as the forthcoming T2HK experiment in addressing these questions. In particular, we evaluate the sensitivity of NO$ u$A to determine neutrino mass hierarchy, octant degeneracy and to obtain CP violation phase after running for its scheduled period of 3 years in neutrino mode and 3 years in anti-neutrino mode. We then extend the analysis to understand the discovery potential if the experiments will run for (5$ u$+5$bar{ u}$) years and (7$ u$+3$bar{ u}$) years. We also show how the sensitivity improves when we combine the data from (3$ u$+3$bar{ u}$) years of NO$ u$A run with (3$ u$+2$bar{ u}$) years of T2K and (3$ u$+7$bar{ u}$) years of T2HK experiments. The CP violation sensitivity is marginal for T2K and NO$ u$A experiments even for ten years data taking of NO$ u$A. T2HK has a significance above 5$sigma$ for a fraction of two-fifth values of the $delta_{CP}$ space. We also find that $delta_{CP}$ can be determined to be better than $35^circ $, $21^circ $ and $9^circ $ for all values of $delta_{CP}$ for T2K, NO$ u$A and T2HK respectively.